Are you staying in Malaga city itself, or one of the resorts down the coast? I've been the Malaga 3x and loved the fact is was a 'city' and a mix of locals and tourists, without the Brit abroad feel that some of the Costa del Sol resorts have.
You can get a bus direct from the airport for 3 euros each (well it was that price a 3yrs ago) to several stops in Malaga city.
Along with the suggestions from @KirkstallAbbess there is also a prommenade along the beach- so you can walk for miles either way on a conrete pathway.
There is a train in Malaga. One of my highlights was a day trip on the train to Ronda. Its a town in the mountains and has the most amazing bridge. I'm not into bridges or structures normally, but it was a a fantastic day seeing the views from the train, and seeing the most amazing bridge completed in 1793. Some lovely shops and restaurants there too.
When are you doing? In summer, they have tavernas on the beach serving freshly grilled sardines.
There is a glass museum which is fascinating
Slightly further away, and I think a bus ride, is the botanical gardens
There are plenty of shops in Malaga itself from high end to smaller independents, so if you like shopping, you will be fine
Mercado de la Merced is a collection of small, independent cafes and restaurants serving various local dishes. You might get croquettas from one place, a tortilla from another and a white wine from a 3rd. very relaxed and friendly. Our 1st time, there were people dancing tango in a nearby open space which was lovely to sit and watch
Near the Mercado is a small bar called Manana Bar. Its up a small alley way, and you might be skeptical, but they were very friendly and serve a mix of ex pats, locals and tourist with a great range of cocktails and drinks to choose from. The owners/managers are 2 brothers who are I think Latvian, but speak English and Spanish also.
Have a fabulous time.